Determination of the 3D border by repeated elimination of internal surfaces

A novel approach to the 3D border determination is presented: it starts by representing the 3D object in linear octtree form, proceeds by eliminating internal boundaries between nodes of the same size while deleting internal nodes and terminates when only border voxels remain. The algorithm basically performs a mapping of the 3D object into its own border, with both input and output being represented as linear octtrees. The algorithm is shown to be executable inO(kn(N+M)) time, wherek andN are the maximum node grouping and number of nodes (respectively) of the initial linear octtree,n is the resolution of the bilevel image andM is the number of border voxels. The range of applicability of the proposed algorithm is quite wide: it can determine the external border of a simply connected region as well as the external and internal borders of a set of multiply connected objects, all at the same time.